Joint maximum likelihood estimation (JMLE) for the hyperbolic cosine model (Andrich & Luo, 1993) is extended to the situation in which the units of items are allowed to vary. Four issues were considered in developing this JMLE procedure: (1) the indeterminacy caused by the unit parameter of each item, (2) a necessary constraint to eliminate this indeterminacy, (3) the initial estimates of the unit and location parameters of the items, and (4) a practical correction procedure to account for inconsistency in parameter estimates. Four estimation cycles were designed to address these issues. Results from two sets of simulation studies (ideal and non-ideal situations) indicated that the algorithm yielded reasonably accurate recovery of the parameters.
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